Jon's misguided solution to fix the tensions between the Northerners and the Wildlings is to eliminate the Free Folk's king, Mance Rayder. Jon believes Rayder is the only component that binds the individual wildling clans that make up their central army and that his death will dissolve their ranks for good. Not only is this plan strategically unsound due to Jon's insistence upon going alone and his decision to leave his Valyrian steel sword with Sam but also the solution doesn't make ethical sense. You don't stop violence with more violence.
However, Jon does manage to get close enough to the Wildling leader to stage an attack — although he's surrounded by Rayder's devoted followers and such a move would mean certain death. Luckily, Jon is literally saved by the bell when war horns signal the arrival of Stannis Baratheon's mounted knights. Stannis wants to retake the North with the help of the wildlings and burns Mance Rayder alive when he refuses to bend the knee. Jon intervenes by putting an arrow in Rayder's heart to keep the man from suffering, a move that inspires debate among the free folk.